More than a half century ago, Bernstein, a neuroscientist, introduced a series of questions related to control of redundant degrees of freedom in the human motor system. (See N. Bernstein, The coordination and regulation of movements, Pergamon, London, 1967, the subject matter of which is incorporated herein by reference in its entirety.) Often referred to as the “degree of freedom” (DOF) problem, Bernstein asked: “How can a neuromuscular system with an exorbitant number of degrees of freedom be made to act as if it had but a few degrees of freedom?” He conjectured that controlled operation of such a system achieves a reduction of mechanical redundancy, effectively by reducing the number of degrees of freedom. Bernstein observed that “dexterity” residing in human motion emerges from accumulated involvement of multi-joint movements in surplus DOFs.
The questions raised by Bernstein have had a profound impact on the analysis and understanding of human motor control. As a result, many established concepts in the theory of human motor development have undergone profound change, and our knowledge has increased greatly. Although many outstanding questions related to “the degree of freedom problem” remain unanswered, the problem has directly or indirectly brought philosophical and physiological insight to many applied science and engineering problems dealing with human and robot motion analysis and control.
Perhaps the most direct analogy of Bernstein's problem has been examined in control of robots which exhibit redundancy with respect to operation of a task. Roboticists have long viewed that redundancy of DOFs with respect to a task enhances dexterity and versatility. Such a notion has been inspirational in the formulation of task oriented control strategies, both at the kinematic and dynamic levels. Redundancy incurs a problem of ill-posedness of inverting the kinematics from task-description space to joint space. In nearly all published material, the ill-posedness of inverse transformations from task space to joint space has been treated by identifying artificial performance indices and determining an inverse kinematics or inverse dynamics solution to minimize it. The appropriate treatment of this ill-posed problem has applications in many disciplines which analyze human motion from low-dimensional motion primitives.
Formalizing Bernstein's conjecture into a control structure allows the representation of the large number of mechanical degrees of freedom involved in the execution of movement tasks to be expressed by lower dimensional motion descriptors. These motion descriptors are sometimes referred to as task descriptors because they are used to describe motion by higher level task variables. In robotics, control policies using task descriptors are generally performed in task space rather than joint space. Task oriented control is compatible with Bernstein's hypothesis and current views in motor learning that suggest the central nervous system organizes or simplifies the control of these degrees of freedom during motion execution and motor learning phase.
As previously stated, controlling tasks generally incurs redundancy when the articulating chain in the mechanism has more degrees of freedom than are required to achieve the task. Many internal joint motions can effectively produce the same desired task motion. The internal self motion manifolds may be keenly utilized to meet additional task requirements besides execution of the task trajectory, thus providing redundancy resolution. The redundancy can be effectively used to keep within joint limits (See C. A. Klein and C. H. Huang, “Review of pseudoinverse control for use with kinematically redundant manipulators,” IEEE Transactions on Systems, Man, and Cybernetics, 13(3):245-250, 1983, the subject matter of which is incorporated herein by reference in its entirety.), to avoid singularities (See T. Yoshikawa, “Manipulability of robot mechanisms,” Int. J. Robotics Research, 4(3):3-9, 1985, the subject matter of which is incorporated herein by reference in its entirety.), to avoid obstacles, and to optimize various other performance criteria.